Prior art concerning with such an automatic transmission is disclosed in Japanese Patent Kokai-Publication No. 58-170955 which proposes a transmission of the type of parallel axis gear arrangement including an electronic control unit into which signals representative of engine revolution speed, brake operation, accelerator pedal position, gear shift lever position, clutch release position and vehicle speed are input, said electronic control unit being adapted to provide output signals for accomplishing throttle opening control, clutch engagement or disengagement and gear shift operation. The transmission furthermore includes a shift and select actuator having three shift shafts for actuating a synchronization mechanism of the transmission gears and a select lever (internal lever) which selectively engages with one of the shift shafts. The shift select actuator is controlled in response to the output signals of the electronic control unit for gear shift operation. Upon setting the position of the shift lever, the electronic control unit automatically operates the clutch engagement or disengagement and gear shift operation in response to the signals representative of engine revolution speed, accelerator pedal position and vehicle speed, wherein the troublesome operation of the clutch pedal is eliminated. Japanese Patent Kokai-Publication No. 58- 170954 discloses also a transmission of the same type as JP-Patent Kokai No. 58-170955.